A337461 Number of pairwise coprime ordered triples of positive integers summing to n.

0, 0, 0, 1, 3, 3, 9, 3, 15, 9, 21, 9, 39, 9, 45, 21, 45, 21, 87, 21, 93, 39, 87, 39, 153, 39, 135, 63, 153, 57, 255, 51, 207, 93, 225, 93, 321, 81, 291, 135, 321, 105, 471, 105, 393, 183, 381, 147, 597, 147, 531, 213, 507, 183, 759, 207, 621, 273, 621, 231

Offset

0,5

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000

Example

The a(3) = 1 through a(9) = 9 triples:
  (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)  (1,1,7)
           (1,2,1)  (1,3,1)  (1,2,3)  (1,5,1)  (1,2,5)  (1,3,5)
           (2,1,1)  (3,1,1)  (1,3,2)  (5,1,1)  (1,3,4)  (1,5,3)
                             (1,4,1)           (1,4,3)  (1,7,1)
                             (2,1,3)           (1,5,2)  (3,1,5)
                             (2,3,1)           (1,6,1)  (3,5,1)
                             (3,1,2)           (2,1,5)  (5,1,3)
                             (3,2,1)           (2,5,1)  (5,3,1)
                             (4,1,1)           (3,1,4)  (7,1,1)
                                               (3,4,1)
                                               (4,1,3)
                                               (4,3,1)
                                               (5,1,2)
                                               (5,2,1)
                                               (6,1,1)

Mathematica

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {3}], CoprimeQ@@#&]], {n, 0, 30}]

Crossrefs

A000212 counts the unimodal instead of coprime version.

A220377*6 is the strict case.

A307719 is the unordered version.

A337462 counts these compositions of any length.

A337563 counts the case of partitions with no 1's.

A337603 only requires the *distinct* parts to be pairwise coprime.

A337604 is the intersecting instead of coprime version.

A014612 ranks 3-part partitions.

A302696 ranks pairwise coprime partitions.

A327516 counts pairwise coprime partitions.

A333228 ranks compositions whose distinct parts are pairwise coprime.

Cf. A000217, A001399, A001840, A014311, A101268, A284825, A337562, A326675, A333227, A337601, A337602.

Sequence in context: A359600 A166466 A068219 * A157031 A113213 A088032

Adjacent sequences: A337458 A337459 A337460 * A337462 A337463 A337464

Keyword

nonn

Author

Gus Wiseman, Sep 02 2020

Status

approved